Both sides in the Brexit debate like to say economics is on their side, claiming Britain will either gain or lose enormous amounts of money if the country votes to leave the EU on June 23.

For years we have been pointing out that there is no definitive cost/benefit analysis.

Now the Treasury has come out with an official report predicting what will happen to the UK economy in the long-term if there is a Leave vote.

Since the government is campaigning for Britain to Stay, today’s intervention is hardly independent, but is it credible?

What’s the Treasury saying?

The argument is that EU membership makes it easier to trade with other member states and nations around the world.

All the realistic alternatives to full EU membership would make it more expensive to trade with EU states and others, so there would be a long-term cost to the UK economy.

The Treasury looks at three alternatives to the status quo and comes up with a cost for each, based on its in-house forecasting model.

If the UK leaves the EU but stays in the European Economic Area – like Norway – the supposed negative effect is 3.8 per cent of GDP a year after 15 years.

If we negotiated a bilateral trade agreement with the bloc – like Switzerland or Canada – GDP might be 6.2 per cent a year lower than expected.

If Britain traded as a WTO member but did not strike a specific trade deal with Brussels it could supposedly expect to lose 7.5 per cent of GDP annually in 2030.

These numbers don’t imply negative growth overall: no one is saying that the UK economy would be smaller than it is now after Brexit. The suggestion is that GDP will not grow as quickly as it would if we stayed in the EU.

The numbers apparently take into account Britain’s multibillion-pound annual contribution to the EU budget. We don’t subtract the membership fee from the supposed loss – it has already been taken into consideration.

Will it really cost every family £4,300?

This is an over-simplification of the government’s argument. It’s numerically correct to say that minus 6.2 per cent of annual GDP (the central estimate of the “Switzerland” scenario) can be divided into £4,300 per household.

But that is using the number of households in the UK now, not 15 years in the future, which is when these numbers are supposed to apply.

And GDP per household isn’t the same as household income. National wealth divided between the population has historically been much higher than average income.

It’s not quite right to say that Brexit “will cost each family £4,300”, since the actual impact on household incomes from a fall in GDP would almost certainly be lower.

How does this compare to other forecasts?

It’s at the pessimistic end of the spectrum, but in the ballpark of what some independent economists have come up with.

A number of think tanks and economists have had a stab at this exercise now, with a broad spectrum of results, but not all are created equal.

Other studies that have used sophisticated forecasting models include this one from the Centre for Economic Performance at the LSE, who predict a loss of GDP of between 2.2 and 9.5 per cent in its most pessimistic scenario.

Losses at the upper end of that scale would be comparable to the effects of the global financial crisis and the authors noted cheerily that “in any case, we should have in mind that these numbers are likely to be larger in reality”.

Oxford Economics looked at nine different post-Brexit scenarios and predicted a long-term cost to the British economy in every case. But the most pessimistic forecast of an annual loss of 3.9 per cent of GDP by 2030 is obviously less than the central Treasury figure.

A spokesman for Oxford Economics was quoted today as saying that some of the assumptions the Treasury had fed into its model (on trade and productivity growth) felt “a little strong” but were not unreasonable.

More optimistic forecasts are available. Open Europe thought there could be either a small loss or gain from Brexit, depending on how Britain met the challenge of trading outside the EU.

Capital Economics also thought there could either be modestly positive or negative impacts, depending on various factors, but were upbeat about the UK’s prospects in or out of the bloc.

At the extreme end of the spectrum, Ukip’s Tim Congdon estimated that EU membership costs this country the equivalent of 10 per cent of GDP, based on an unusually high assessment of the cost of regulation from Brussels.

What are the main criticisms?

Immigration: the Treasury’s analysis is based on the assumption that net migration to the UK will remain high, contrary to the Conservatives’ current aspiration to reduce it to the “tens of thousands”, and even after a vote for Brexit.

Jonathan Portes from the think-tank NIESR said: “Given the centrality of immigration and free movement in the political debate on Brexit, this is difficult to understand.”

Red tape: Other critics say the Treasury has skated over the issue of the cost to Britain of EU regulations.

The report doesn’t actually attempt to put a figure on the cost of red tape. But it concludes that “any gains from increased flexibility in specific areas would be significantly outweighed by the losses from increased regulatory barriers to trade from losing access to the single market”.

Uncertainty: economic modelling like this looks at the past to figure out the benefits of membership of the EU, and attempts to say what would have happened to trade if Britain had not joined.

That’s not quite the same as looking at the true cost of a country actually pulling out of the bloc – something which has never happened before and is even more difficult to predict.

The verdict

The Treasury paper offers a pessimistic view of what might happen to Britain if we left the EU, but one that is broadly in line with what some independent models have come up with.

It’s important to bear in mind that these models are largely based on the assumption that Britain will be less open to trade after Brexit. And of course, many people don’t buy this, believing that the UK will have more freedom to strike trade deals with emerging economies.

If you don’t accept the central premise that Brexit will hurt trade, you won’t believe any of the numbers the government has put out today. Or you might think that a drop in potential GDP growth is a price worth paying for more control over immigration.

Economically, much depends on what kind of trade deals Britain would be able to negotiate with EU countries and others after a Leave vote.

Since there is no precedent for Brexit, it’s very hard for anyone to make a confident prediction about what will happen.